A138608 List first F(1) numbers from A016777, then first F(2) numbers from A016789, then the first F(3) numbers from A008585 (starting from 3), then the next F(4) numbers from A016777, then the next F(5) numbers from A016789, then the next F(6) numbers from A008585, etc, where F(n) = A000045(n), the n-th Fibonacci number.

1, 2, 3, 6, 4, 7, 10, 5, 8, 11, 14, 17, 9, 12, 15, 18, 21, 24, 27, 30, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84

Offset

1,2

Comments

The original name was "Generalized FibCon sequence". However, this sequence has only a passing resemblance to Connell-like sequences (see A001614 and the paper by Iannucci & Mills-Taylor), which are all monotone, while this sequence is a bijection of natural numbers.

Links

Table of n, a(n) for n=1..72.

Douglas E. Iannucci, Donna Mills-Taylor, On Generalizing the Connell Sequence, Journal of Integer Sequences, Vol. 2 (1999), Article 99.1.7

Index entries for sequences that are permutations of the natural numbers

Formula

If n < 4, a(n) = n. If n = A000045(A072649(n)+1), then a(n) = a(n-1-A000045(A072649(n)))+3, otherwise a(n) = a(n-1)+3. - Antti Karttunen, Oct 05 2009

1. The sequence is formed by concatenating subsequences S0,S1, S2, ..., each of finite length. 2. The subsequence S0 consists of the element 1. 3. The n-th subsequence has F(n) elements, F(n) denotes n-th Fibonacci number. 4. Each subsequence is nondecreasing and the difference between two consecutive elements in the same subsequence is 3.

Example

Let us separate natural numbers into three disjoint sets (A016777, A016789 and A008585):
  1,4,7,10,13,16,19,22,25,28,31,...
  2,5,8,11,14,17,20,23,26,29,32,...
  3,6,9,12,15,18,21,24,27,30,33,...
then
  S0={1}
  S1={2}
  S2={3,6}
  S3={4,7,10}
  S4={5,8,11,14,17}
  S5={9,12,15,18,21,24,27,30}
  ...
and concatenating S0/S1/S2/S3/S4/S5/... gives this sequence.

Prog

(Scheme) (define (A138608 n) (if (< n 4) n (let ((k (A072649 n))) (if (= n (A000045 (1+ k))) (+ 3 (A138608 (- n 1 (A000045 k)))) (+ 3 (A138608 (-1+ n)))))))

Crossrefs

Inverse: A166015. A010872(a(n)) = A010872(A072649(n)). Cf. A138606-A138609, A138612.

Sequence in context: A019567 A098286 A226615 * A092283 A266191 A273338

Adjacent sequences: A138605 A138606 A138607 * A138609 A138610 A138611

Keyword

easy,nonn

Author

Ctibor O. Zizka, May 14 2008

Extensions

Edited, extended, starting offset changed from 0 to 1, and Scheme-code added by Antti Karttunen, Oct 05 2009

Status

approved